Methods for calculating the pressure loss of the air flow and energy consumed by the fan of the cotton harvester

The article presents the methods for calculating the pressure loss of the pneumatic transport system of a cotton harvester related to the power consumption of the fan drive. Mathematical models for computer calculation are presented. Numerical studies of the influence of the pipeline diameter and the air mixture composition on the power consumption of the fan drive are presented. It was determined that with an increase in the diameter of the pipeline from 0.15 m to 0.175 m and a change in the mixture concentration μ = 0.228 ÷ 0.338 for a serial receiving chamber, the fan drive power decreases from 10.3 kW to 5.79 kW.


Introduction
Improving the efficiency of the pneumatic transport system of the cotton harvester while maintaining the biological qualities of cotton, with less loss of raw material and less power consumption of the fan drive, is a relevant aspect. However, no attention was paid to the development of mathematical models to effectively use the pneumatic transport system [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].
In this regard, the development of mathematical models for the pneumatic transport system of the cotton-harvesting machine is the goal of this article.
When air moves in pipelines, internal and external friction forces of its individual particles or layers arise. Air has a viscosity, which manifests itself in the form of internal friction forces induced by relative displacement of its adjacent layers. External friction forces arise from the contact of moving air particles with the pipeline walls.
When a mixture of air and raw material moves in pipes, pressure losses increase due to the need to impart acceleration to the particles of the material, to compensate for the energy consumption to lift the particles and to restore the velocity of the particles of the solid component when they interact with the wall material of the pipe and with each other. Therefore, the pressure loss is a consequence of flow resistance (air drag).
When transporting raw cotton, there are different unfavorable areas; one of them is the pipe-bend. As noted by F.G. Zuev [16], when the flow moves along the pipe-bend, pressure losses consist of the sum of losses due to friction and air vortices at the flow turn, friction of solid particles against the material of the pipe wall, inertial forces of the flow components and velocity loss during a turn.
Aerodynamic calculations for the cotton transport in cotton harvesters XN-3,6 were given by N.A. Artykov in [17]. However, the study did not consider the different values of the pressure loss in the pipelines connected to a single fan.
Different values of pressure loss occur due to the difference in the pipeline lengths and the number of pipe-bends that connect the cotton receiving chamber to the air collector. Besides, the chamber located on the front spindle drums receives more raw cotton than the rear receiving chambers; this also affects the pressure loss. The authors of that article in the calculation method did not consider the air suction from the leaky pipeline connections. In this regard, it is necessary to improve the calculation methods given in [18], considering the above disadvantages.

Materials and Methods
For the aerodynamic calculation of the pneumatic transport system of the cotton harvester, the following data are required: characteristics of the material, productivity, total pressure, and pipeline route (rise of height, presence of pipe-bends). It is necessary to select the concentration of the mixture, to determine the air velocity, the pressure loss in the pipeline network, and to calculate the corresponding power consumption of the fan (for 14XV.61.020.A and 14XV.61.060A harvesters). Therefore, we determine the pressure loss in all elements of the pneumatic transport system for CHM MX-2.4, Figure 1. The pressure loss at the inflow of the cotton mixture into the receiving chamber is: where:   is the air flow velocity in the pipeline, m/s;   is the air density, (ρ = 1.29 kg/m 3 ); β -is the coefficient of pressure loss during acceleration of the material, (β = 1.8 + 1.5 m) [13] The pressure loss in the pipe-bend is determined as: where:   are the resistance coefficients of the bend.
According to [17], М = 0.274 ТР = 0.008 Т = (0.087 + 0.37), the pressure loss in the inclined section is determined as: According to [18], e R is determined as: where:   is the flow rate; D  is the diameter of a circular air pipe;   is the gas kinematic viscosity coefficient; According to [17], Pressurelossunder the impact at the entrance to the bend section is: where: . Pressure loss at the turning section where it is connected by centrifugal fans is where:  is the coefficient that takes into account the confluence of flows; according to [19], it is Pressure loss in diffuser and fan outlet is: where: where: Н  is the rise of the height of the material, m;   8 P is the pressure loss for the suction of the pipeline system from the total volume of 1 1.01 k   [19].
Based on the above calculation method, the total pressure loss of each pipeline is determined as: We determine the average pressure loss of pipelines connected to a single fan as: Determine the power consumption of the fan drive:

Development of a mathematical model
To develop a mathematical model for determining the power consumption of the fan drive, we assume that: Р is pressure loss at the suction of the pneumatic conveying system   Pressure loss in four pipelines is:

Results of numerical studies
For numerical studies, we use the programs developed in [20]. To determine the effect of the concentration of the air mixture on the power consumption of the fan drive, we assume that: Serialreceivingchamber(Q 1 =0.55m 3 Figure 2. To determine the influence of the pipeline diameter (D) and the concentration of the air mixture (μ) on the power consumption of the drive, we assume that the initial data are: Serial receiving chamber (Q 1 =0.55m 3     From the graphs in Figure 2, it is seen that an increase in the concentration of the air mixture (μ) leads to an increase in the fan drive power consumed when using an experimental serial version of the receiving chamber. However, for the serial receiving chamber, the power consumption of the fan drive is 1.66 times higher than the consumption of the experimental receiving chamber. From the graphs in Figure 3, it is seen that an increase in pipeline diameter from 0.  Figure 4 shows the effect of the change in the pipeline's diameter and the concentration of the air mixture (μ) on the fan drive power of the experimental receiving chamber. The patterns of graph changes are similar to the patterns in Figure 3; however, the power consumption of the fan drive is1.65 times less compared to the serial receiving chambers.

Conclusions
To reduce the power consumption of the fan drive, it is necessary to use a pipeline with a diameter of at least D= 0.175 m. The use of an experimental receiving chamber instead of a serial chamber allows us to reduce the power consumption of the fan drive by 1.65 times. With an increase in the pipeline's diameter from 0.15 m to 0.175 m, the effect of the air mixture composition on the power consumption of the drive decreases by 1.77 times.